A hydroprocessing trickle reactor construction which will facilitate the catalytic dewaxing of liquid petroleum or lube feedstocks in a highly efficient and economical manner, particularly through the use of reactors employing stationary bed of a defined, shape-selective crystalline aluminosilicate zeolite catalyst, preferably ZSM-5. Pursuant to one embodiment of the hydroprocessing reactor, the latter is essentially constituted of a trickle bed reactor wherein a plurality of vertically tiered and staggered trays support the beds of catalyst material, such as the crystalline zeolite, and through which the liquid petroleum feedstock trickles downwardly from the upper end of the reactor, while hydrogen is concurrently injected into the catalyst on each of the trays. This causes the hydrogen to percolate through the catalyst bed and to contact and efficiently strip the downwardly trickling stream of liquid petroleum feedstock of low boiling conversion products or waxy components, such as naphtha. Pursuant to a second embodiment of the hydroprocessing catalystic reactor construction, inclined supporting stationary beds of catalyst are vertically tiered with the liquid petroleum stock trickling down through the reactor so as to enter the upper portion of the bed contained in each tray, flowing along the inclined tray surface thereof forming a liquid seal along the bottom surface of each tray and forcing hydrogen introduced into each tray to flow upwardly through the catalyst bed and react with the liquid petroleum feedstock. The liquid is directed to trickle downwardly to a lower catalyst bed through the interposition of suitable baffles, whereas hydrogen gas inclusive of low boiling, volatile conversion products stripped from the liquid petroleum in the catalyst beds flows upwardly through passages beneath the baffles into a central vertical conduit in the reactor, from when they are conducted by being entrained in an upwardly-flowing carrier gas out of the upper end of the reactor.